The field of polynomial systems occupies a central role in computational mathematics, where the intricate interplay between algebra, geometry, and computational complexity is evident. Research in this ...

Two mathematicians have used a new geometric approach in order to address a very old problem in algebra. In school, we often learn how to multiply out and factor polynomial equations like (x² – 1) or ...

Two mathematicians have used a new geometric approach in order to address a very old problem in algebra. In school, we often learn how to multiply out and factor polynomial equations like (x² – 1) or ...

For centuries, one of algebra’s oldest puzzles has remained unsolved—how to find exact answers for higher-degree polynomials, where the variable is raised to the fifth power or more. Mathematicians ...

Polynomials are equations in which a variable is raised to different powers, like 1 + 4x—3x² = 0 (a degree-two polynomial). These equations are essential in math and science, helping explain things ...

A mathematician has built an algebraic solution to an equation that was once believed impossible to solve. The equations are fundamental to maths as well as science, where they have broad applications ...

A UNSW mathematician has developed a novel method to to tackle algebra’s oldest challenge – solving higher polynomial equations. Polynomials, involving variables raised to powers, are crucial in ...

In this paper, an efficient method is presented for solving two dimensional Fredholm and Volterra integral equations of the second kind. Chebyshev polynomials are applied to approximate a solution for ...

Abstract: The solution of overdetermined systems of polynomial equations shows promise for solving complicated problems in signal processing and related fields. Polynomials can represent more ...

In a factorial ring, we can define the p.g.c.d. of two elements (defined to the nearest unit) and the notion of prime elements between them. More generally, Bezout’s identity characterizes two prime ...